Many manufacturing processes have specification limits, or process parameters, that can be more important to enforce in one direction than in the other, relative to the specification limit. For example, a material removal process such as ion milling or chemical mechanical planarization (CMP) on a wafer can have a specification limit/target related to wafer thickness. If not enough material is removed to meet the specification target thickness, the wafer can be reworked to remove additional material. However, if too much material is removed, the wafer may need to be scrapped, which is far more expensive than removing less material than necessary to meet the target thickness. In this case, it makes sense to err on the side of removing less than the target thickness. At the same time, there is generally a requirement to keep the process centered on the specification limit/target.
Processes employing exponential weighted moving average (EWMA) type filters have been used in conjunction with run to run type control to track and adjust the critical process parameters if they drift. However, these known processes do not adequately address the above described problem of asymmetric risk for a process parameter.